A BVA will be granted immediately after applying for the 820/801.
The BVA will have full work rights, even if you get it from an 820/801 app from a visitor visa.
The BVA goes into effect when the current stay period of the visitor visa expires and you are still onshore. So if you have 3 month stay periods and you apply for the 820/801, then you would essentially overstay that stay period for the BVA to kick in. It's not the expiry of the visa itself.
Edit: Congrats on your engagement! Keep in mind of the third visa option available for engaged couples, the subclass 300. Best for those that don't qualify as de facto.
I always throw it out there because people don't seem to be aware of it.
Dating and de facto are two different things. The latter is required for an 820/801 and easiest way to prove it is to live together and have combined lives such as joint lease/mortgage, bank accounts, etc. Hard to tell if you'd meet the requirements or if it would be considered dating, but a migration agent can certainly look what you have over and tell you if you'd meet the requirements or not.
PMV route is only $1170 more expensive and does not require de facto evidence so is often the only real partner visa route for engaged couples, especially those that live apart. No point in doing it if you definitely qualify as de facto as you can apply for the 820/801 as a couple, as an engaged couple, or as a married couple. The evidence requirement is the same regardless.
If at the time of application the couple can prove to have been de facto for at least three years prior to applying, then yes the CO can choose to grant the 801 along with 820. This doesn't always seem to happen though and is at the discretion of the CO. Also, that is 3 years DE FACTO. Time dating does not count and it's all about whether a CO thinks what evidence you have is dating or de facto. There are couples who have posted on here recently who showed de facto evidence for 3+ years and still were only granted the 820, so i wouldn't bank on jumping straight to PR without solid evidence.
The 3 years thing like I said above but you don't apply for just PR.
You have to make a combined 820/801 application. You wait the normal wait times for the 820 processing times. A CO assesses your applicatipn and can choose, at their discretion, whether you meet that long term relationship requirement.
If no, you get the 820 grant and are eligible for the 801 PR two years from the time ypu made the initial 820/801 application.
If yes, they grant the 820 and then immediately grant the 801, waiving that 2 year wait period for eligibility.
There's no way to skip the 820 stage or wait times.
If you plan on trying to get PR quicker that way, you should seriously consider having an RMA present your application for you. Or at least discuss that with them now and they can look over what evidence you do have to see if that's even an option for you. Your evidence may or may not be strong enough and if it's not, then there's no point in waiting until the 3 year anniversary to apply.